A364544 Numbers k such that k divides A005940(k).

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 125, 128, 160, 192, 245, 250, 256, 320, 375, 384, 490, 500, 512, 640, 715, 750, 768, 845, 847, 980, 1000, 1024, 1215, 1280, 1430, 1500, 1536, 1690, 1694, 1960, 2000, 2048, 2430, 2560, 2860, 2873, 3000, 3072, 3380, 3388, 3920, 4000, 4096, 4860, 5120

Offset: 1

Author

Antti Karttunen, Jul 28 2023

Keywords

• nonn

Comments

If k is a term, then also 2*k is present in this sequence, and vice versa.

A029747 is included as a subsequence, because it gives the known fixed points of map n -> A005940(n).

Crossrefs

Positions of 1's in A364501.

Subsequence of A364542.

Subsequences: A029747, A364545 (odd terms).

Cf. A005940.

Cf. also A364494, A364546.

Programs

Mathematica

nn = 5120; Array[Set[a[#], #] &, 2]; Do[If[EvenQ[n], Set[a[n], 2 a[n/2]], Set[a[n], Times @@ Power @@@ Map[{Prime[PrimePi[#1] + 1], #2} & @@ # &, FactorInteger[a[(n + 1)/2]]]]], {n, 3, nn}]; Select[Range[nn], Divisible[a[#], #] &] (* Michael De Vlieger, Jul 28 2023 *)

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
isA364544(n) = !(A005940(n)%n);